Exact solutions for a periodic assembly of bubbles in a Hele-Shaw channel
Fluid Dynamics
2014-04-10 v1 Mathematical Physics
math.MP
Pattern Formation and Solitons
Abstract
Exact solutions are reported for a periodic assembly of bubbles steadily co-travelling in a Hele-Shaw channel. The solutions are obtained as conformal mappings from a multiply connected circular domain in an auxiliary complex plane to the flow region in a period cell. The conformal mappings are constructed using the generalized Schwarz-Christoffel formula for multiply connected polygonal domains in terms of products of Schottky-Klein prime functions. It is shown that previous solutions for multiple steady bubbles in a Hele-Shaw cell are all particular cases of the solutions described herein. Examples of specific bubble configurations are discussed.
Keywords
Cite
@article{arxiv.1404.2312,
title = {Exact solutions for a periodic assembly of bubbles in a Hele-Shaw channel},
author = {Giovani L. Vasconcelos and Christopher C. Green},
journal= {arXiv preprint arXiv:1404.2312},
year = {2014}
}
Comments
11 pages, 2 figures